Stop!  This post contains spoilers.  This page has the solution to the problem posed in yesterday’s post. We challenged you to find a set from which we can make as many new sets as possible using only the closure and complement operations. In 1922 Kuratowski proved the following theorem. Theorem. At most 14 sets can…

One of my favorite theorems in elementary topology is Kuratowski’s closure-complement theorem. First some notation.  For any set let denote the complement of and  denote the closure of .  (Recall that and  is the union of and all the limit points of ). Here’s the problem.  Find a set so that we can construct as many…